MHT CET20225 Aug 2022Evening ShiftMathematicsIndefinite IntegrationActual
x^ 2 x (1+2 x) d x= (where C is a constant of integration.)
Options
- Ae^ 2 x 1+2 x +C
- Be^ 2 x 4(1+2 x) +C
- C4 e^ 2 x 1+2 x +C
- De^ 2 x 2(1+2 x) +C
Correct answer
B. e^ 2 x 4(1+2 x) +C
Step-by-step solution
x e^ 2 x (1+2 x)^2 d x Let 2 x = t 2 dx = dt aligned & = 1 4 2 x e ^ 2 x (1+2 x )^2 2 dx & = 1 4 te dt (1+ t )^2 & = 1 4 e ^ t 1 1+ t - 1 (1+ t )^2 dt & = 1 4 e ^ t 1 1+ t + C [ e ^ x f ( x )+ f ^ ( x ) dx = e ^ xf ( x )+ C ] aligned